Johannes Kepler (1571-1630)

Kepler was able to make so significant a contribution
to astronomy and physics because of the precise data he had acquired from
Tycho Brahe. Kepler was a Copernican and also originally believed that
the planets should follow perfectly circular orbits. In fact, in Copernicus'
time the state of the astronomical art in locating planets was accurate
to 10' ( 10 minutes of arc). With this level of accuracy which could be measured for the planets
the circular orbit was acceptable. Brahe, however,
made measurements accurate to 2' of arc. Brahe had his own system of the
world, in which the earth was the center and the sun revolved around the
earth with the planets revolving about the sun. In order to prove his system,
or to settle between the Copernican and Ptolemaic system he set out on
precision measurements of the locations of the planets. Brahe did not use
a telescope, so his method of observation was quickly superseded by the
telescopic investigations which began about ten years after his death.
Nevertheless, his observations for 777 stars and the planet Mars have
only been fractionally improved today.

"Tycho was a foul-tempered Danish lord who tongue-lashed
kings, tormented peasants, sported a silver nose ( his own having been
lost in a youthful duel over mathematics), and kept a clairvoyant dwarf
as a court jester and a tame elk that got drunk one night, fell down stairs,
broke a leg and died. Yet Tycho was a measuring maniac, a fussily precise
man who opened a new age of observation in science." ( p. 432)

Because of a disagreement with the new Danish King
Christian IV, he left his island observatory, Uraniborg and went to Prague
in 1597 to take up an appointment as Imperial Mathematician for Rudolph
II. In 1600 Kepler joined Brahe. Kepler was a mystic who sought to develop
cosmology and he knew he needed access to Brahe's excellent data. Brahe
knew that Kepler was quite skilled in mathematics and hoped Kepler would
organize his data in a useful form. Despite this mutual need it seems that
Brahe kept his data away from Kepler. About 1 1/2 years later Brahe died
from an acute urinary infection. His last words to Kepler were, "Let me
not seem to have lived in vain."

Immediately after Brahe's death Kepler secretly took
away Brahe's data so that they would not be lost in the settlement of Brahe's
estate. Kepler was appointed to the now vacant post of imperial mathematician.
In 1627 Kepler finally published a full set of tables that came from Brahe's
data called the Rudolphine Tables.

For six years following Brahe's death Kepler was at
war with the planet Mars. Mars showed greater irregularities of motion
than the other planets. Kepler sought to find the curved orbit around the
sun that would describe Mars' orbit. This was a daunting task since his
observations were of a moving body taken from a moving observatory( the
earth). In his book, Astronomia Nova, he describes the techniques
he devised to establish the orbit of Mars. Brahe's data, collected over
a period of some 25 years, was enough to allow Kepler to determine twelve
points on the orbit of Mars. However, he could not force a circular orbit
to go through those points. Indeed, the orbit turned out to be elliptical.
The best circular orbit he could fit through the data would have produced
observational errors of 8' of arc. Here the precision of Brahe's data was
absolutely crucial. Not only were these accurate data needed, but also
a conceptual break and high integrity on Kepler's part to accept the data
for what they said. A circular orbit for Mars is out of the question. Kepler
chose to believe the observations, rather than the Platonic ideal of circular
motion. These observations were to be
crucial for the tests of Newton'stheory of Universal Gravitation some eighty years later.

"I was almost driven to madness in considering and
calculating the matter. I could not find out why the planet (Mars) would
rather go on an elliptical orbit.... With reasoning derived from physical
principles agreeing with experience, there is no figure left for the orbit
of the planet except for a perfect ellipse.... Why should I mince words?
The truth of Nature, which I had rejected and chased away, returned by
stealth through the back door, disguising itself to be accepted....I thought
and searched, until I went nearly mad, for a reason why the planet
preferred an elliptical orbit."

Johannes Kepler was born in Weil der Stadt in Swabia, in southwest
Germany. His paternal grandfather, Sebald Kepler, was a respected craftsman
who served as mayor of the city; his maternal grandfather, Melchior Guldenmann,
was an innkeeper and mayor of the nearby village of Eltingen. His father,
Heinrich Kepler, was "an immoral, rough and quarrelsome soldier," according
to Kepler, and he described his mother in similar unflattering terms. From
1574 to 1576 Johannes lived with his grandparents; in 1576 his parents
moved to nearby Leonberg, where Johannes entered the Latin school. In 1584
he entered the Protestant seminary at Adelberg, and in 1589 he began his
university education at the Protestant university of Tübingen. Here
he studied theology and read widely. He passed the M.A. examination in
1591 and continued his studies as a graduate student.

Kepler's teacher in the mathematical subjects was Michael Maestlin
(1580-1635). Maestlin was one of the earliest astronomers to subscribe
to Copernicus's heliocentric theory, although in his university lectures
he taught only the Ptolemaic system. Only in what we might call graduate
seminars did he acquaint his students, among whom was Kepler, with the
technical details of the Copernican. Kepler stated later that at
this time he became a Copernican for "physical or, if you prefer, metaphysical
reasons."

In 1594 Kepler accepted an appointment as professor of mathematics
at the Protestant seminary in Graz (in the Austrian province of Styria).
He was also appointed district mathematician and calendar maker. Kepler
remained in Graz until 1600, when all Protestants were forced to convert
to Catholicism or leave the province, as part of Counter Reformation
measures. For six years, Kepler taught arithmetic, geometry (when there
were interested students), Virgil, and rhetoric. In his spare time he pursued
his private studies in astronomy and astrology. In 1597 Kepler married
Barbara Müller. In that same year he published his first important
work, The Cosmographic Mystery, in which he argued that the distances
of the planets from the Sun in the Copernican system were determined by
the five regular solids, if one supposed that a planet's orbit was circumscribed
about one solid and inscribed in another.

Except for Mercury, Kepler's construction produced remarkably
accurate results. Because of his talent as a mathematician, displayed in
this volume, Kepler was invited by Tycho Brahe to Prague to become his
assistant and calculate new orbits for the planets from Tycho's observations.
Kepler moved to Prague in 1600.

Kepler served as Tycho Brahe's assistant until the latter's death
in 1601 and was then appointed Tycho's successor as Imperial Mathematician,
the most prestigious appointment in mathematics in Europe. He occupied
this post until, in 1612, Emperor Rudolph II was deposed. In Prague Kepler
published a number of important books. In 1604 Astronomia pars Optica
("The Optical Part of Astronomy") appeared, in which he treated atmospheric
refraction but also treated lenses and gave the modern explanation of the
workings of the eye; in 1606 he published De Stella Nova ("Concerning
the New Star") on the new star that had appeared in 1604; and in 1609 his
Astronomia Nova ("New Astronomy") appeared, which contained his
first two laws (planets move in elliptical orbits with the sun as one of
the foci, and a planet sweeps out equal areas in equal times). Whereas
other astronomers still followed the ancient precept that the study of
the planets is a problem only in kinematics, Kepler took an openly dynamic
approach, introducing physics into the heavens.

In 1610 Kepler heard and read about Galileo's discoveries with
the spyglass. He quickly composed a long letter of support which he published
as Dissertatio cum Nuncio Sidereo ("Conversation with the Sidereal
Messenger"), and when, later that year, he obtained the use of a suitable
telescope, he published his observations of Jupiter's satellites under
the title Narratio de Observatis Quatuor Jovis Satellitibus ("Narration
about Four Satellites of Jupiter observed"). These tracts were an enormous
support to Galileo, whose discoveries were doubted or denied by many. Both
of Kepler's tracts were quickly reprinted in Florence. Kepler went on to
provide the beginning of a theory of the telescope in his Dioptrice,
published in 1611.

During this period the Keplers had three children (two had been born
in Graz but died within months), Susanna (1602), who married Kepler's assistant
Jakob Bartsch in 1630, Friedrich (1604-1611), and Ludwig (1607-1663). Kepler's
wife, Barbara, died in 1612. In that year Kepler accepted the position
of district mathematician in the city of Linz, a position he occupied until
1626. In Linz Kepler married Susanna Reuttinger. The couple had six children,
of whom three died very early.

In Linz Kepler published first a work on chronology and the year of
Jesus's birth, In German in 1613 and more amply in Latin in 1614: De
Vero Anno quo Aeternus Dei Filius Humanam Naturam in Utero Benedictae Virginis
Mariae Assumpsit (Concerning the True Year in which the Son of God
assumed a Human Nature in the Uterus of the Blessed Virgin Mary"). In this
work Kepler demonstrated that the Christian calendar was in error by five
years, and that Jesus had been born in 4 BC, a conclusion that is now universally
accepted. Between 1617 and 1621 Kepler published Epitome Astronomiae
Copernicanae ("Epitome of Copernican Astronomy"), which became the
most influential introduction to heliocentric astronomy; in 1619 he published
Harmonice Mundi ("Harmony of the World"), in which he derived the
heliocentric distances of the planets and their periods from considerations
of musical harmony. In this work we find his third law, relating the periods
of the planets to their mean orbital radii.

In 1615-16 there was a witch hunt in Kepler's native region, and
his own mother was accused of being a witch. It was not until late in 1620
that the proceedings against her ended with her being set free. At her
trial, her defense was conducted by her son Johannes.

1618 marked the beginning of the Thirty Years War, a war that
devastated the German and Austrian region. Kepler's position in Linz now
became progressively worse, as Counter Reformation Counter Reformation
measures put pressure on Protestants in the Upper Austria province of which
Linz was the capital. Because he was a court official, Kepler was exempted
from a decree that banished all Protestants from the province, but he nevertheless
suffered persecution. During this time Kepler was having his Tabulae
Rudolphinae ("Rudolphine Tables") printed, the new tables, based on
Tycho Brahe's accurate observations, calculated according to Kepler's elliptical
astronomy. When a peasant rebellion broke out and Linz was besieged, a
fire destroyed the printer's house and shop, and with it much of the printed
edition. Soldiers were garrisoned in Kepler's house. He and his family
left Linz in 1626. The Tabulae Rudolphinae were published in Ulm
in 1627.

Kepler now had no position and no salary. He tried to obtain appointments
from various courts and returned to Prague in an effort to pry salary that
was owed him from his years as Imperial Mathematician from the imperial
treasury. He died in Regensburg in 1630. Besides the works mentioned here,
Kepler published numerous smaller works on a variety of subjects.